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Guidelines_English_Final

الموقع العربي

 

Math 583-1 Advanced Functional Analysis 4(3+1)

Spectrum of an operator, compact linear operators and their spectral properties, spectral properties of bounded self-adjoint operators, positive operators, product of positive operators, square root of positive operator, projection operators: Theorem (positivity, norm), Theorem (partial order), Theorem (product of projections), Theorem ( sum of projections), Theorem (difference of projections), Spectral family of a bounded self-adjoint operator, Banach algebras, Gelfand’ mapping, spectral theorem for normal operators.

 

 References:

1.   E. Kreyszig, "Introductory Functional analysis with Applications", John Wiley & sons, 1978.

E-Kreyszig Introductory Functional

2.   K. Zhu, An Introduction to Operator Algebras, CRC Press, 1993.

3.   I. Gohberg and S. Goldberg, Basic Operator Theory, Birkhauser, 1980.

4.   W. Rudin, "Functional Analysis", McGraw-Hill, Inc., 1991.

5.   C. Swarz, "An Introduction to Functional Analysis", Marcel Dekker, 1992.

6.   Taylor and D. C. Lay, "Introduction to Functional Analysis", John Wiley & sons, 1980.

 

 

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